TY - JOUR
T1 - Optimal open-loop strategies in a debt management problem
AU - Bressan, Alberto
AU - Jiang, Yilun
N1 - Publisher Copyright:
© 2018 World Scientific Publishing Company.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - The paper studies optimal strategies for a borrower who needs to repay his debt, in an infinite time horizon. An instantaneous bankruptcy risk is present, which increases with the size of the debt. This induces a pool of risk-neutral lenders to charge a higher interest rate, to compensate for the possible loss of part of their investment. Solutions are interpreted as Stackelberg equilibria, where the borrower announces his repayment strategy u(t) at all future times, and lenders adjust the interest rate accordingly. This yields a highly non-standard problem of optimal control, where the instantaneous dynamics depend on the entire future evolution of the system. Our analysis shows the existence of optimal open-loop controls, deriving necessary conditions for optimality and characterizing possible asymptotic limits as t +∞.
AB - The paper studies optimal strategies for a borrower who needs to repay his debt, in an infinite time horizon. An instantaneous bankruptcy risk is present, which increases with the size of the debt. This induces a pool of risk-neutral lenders to charge a higher interest rate, to compensate for the possible loss of part of their investment. Solutions are interpreted as Stackelberg equilibria, where the borrower announces his repayment strategy u(t) at all future times, and lenders adjust the interest rate accordingly. This yields a highly non-standard problem of optimal control, where the instantaneous dynamics depend on the entire future evolution of the system. Our analysis shows the existence of optimal open-loop controls, deriving necessary conditions for optimality and characterizing possible asymptotic limits as t +∞.
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U2 - 10.1142/S0219530517500038
DO - 10.1142/S0219530517500038
M3 - Article
AN - SCOPUS:85032215805
SN - 0219-5305
VL - 16
SP - 133
EP - 157
JO - Analysis and Applications
JF - Analysis and Applications
IS - 1
ER -